Electrical, electronic, and electromechanical systems are often required to transmit a wide range of signal frequencies. However, an imperfect system frequency response can result from inherent characteristics of any component in the overall system. For example, the failure of microphones, loudspeakers and listening spaces (auditoria, studios, etc.) to provide truly flat frequency responses over the full audio frequency range is common and well known. This creates a need for electrical or electronic circuits to complement and correct these frequency response deviations. Such correcting circuits are conventionally called "equalizers" or "equalizer networks" because, when inserted in a system, they provide for a more "equal" response of the system over a specified frequency range. Of course, such "equalizers" may also be used to create an imbalance in the frequency response of a system to meet some special requirement or preference.
Traditionally, equalizers have been designed and realized by two techniques. The first requires a person skilled in the art of empirical filter design. The imperfect system frequency response is examined and a complementary filter is assembled by trial and error. This technique is tedious and time consuming; moreover, it is often impractical and inadequate if precise equalization or precision conformance to a given frequency characteristic are required.
The second conventional equalizer network technique uses a multiplicity of simple resonant circuits. Each circuit is tuned to a given frequency such that a set of such circuits covers the entire frequency range to be equalized. These circuits may comprise band pass filters or band rejection filters. By adjusting the contribution of each filter to the total output, a controlled frequency response is accomplished. Davis et al U.S. Pat. No. 3,624,298 shows a system of this kind, using a set of band rejection filters spaced on one-third octave frequency centers, intended for equalizing a sound reinforcement system. A principal shortcoming of this technique is the superposition of the responses of the individual band filters upon the desired equalized response. Thus, the overall response shows bumps and dips at transition points where the response crosses over from one filter to another. Also, the transient response shows ringing from the individual filters in the equalizer output. To minimize the magnitude of these bumps and dips and transient ringing, the individual filters can be less sharply tuned or can be spaced closer together, or both. This, however, results in a system in which a given band of the overall frequency range is responsive to several adjacent filters and requires many reiterative adjustments among the adjacent band controls.
Wiener and Lee U.S. Pat. No. 2,024,900 and Lee and Wiener U.S. Pat. No. 2,128,257 describe a technique for synthesizing frequency responsive networks by means of orthonormal functions. In particular, these patents disclose a technique for representing any desired frequency response in a Fourier series which is composed of the sins/cosine orthonormal functions. Moreover, they describe an all pass passive ladder network which provides a frequency response described by such a Fourier series. Finally, they show that the coefficients in the Fourier series representing the desired frequency response can be directly related to scaling resistors in the all pass ladder network. In this manner, Wiener and Lee devised a system of adjustable equalizers using passive ladder networks and mechanically ganged potentiometers. That system, although theoretically workable, is extremely unwieldly to implement.
The Wiener and Lee equalizer networks constitute filters that are each symmetrical relative to a given center point; each filter network includes an even number of sections with the two center sections being of corresponding construction, the next two sections having the same parameters, and so on. A substantial problem, in a symmetrical equalizer system like that proposed by Wiener and Lee, is the need for impedance matching between adjacent sections, which may be quite difficult. That basic problem can be alleviated by replacing the passive ladder network filters of Wiener and Lee with active operational amplifier circuits, specifically first order all pass amplifiers, as in the filters proposed by G. D. Tattersall in the brief article "Linear Phase Analog Active Filters with Equiripple Passband Responses" in IEEE Transactions on Circuits and Systems, Vol. CAS-28, No. 9, September, 1981, pp. 925-927. The Tattersall filters, like those of Wiener and Lee, are of symmetrical construction, and are configured to afford approximately the same degree of ripple in the rejection band as in the pass band of the filter.
The Tattersall technique affords a linear phase transversal filter in which all frequencies are delayed by the same amount regardless of whether they are filtered (attenuated) or not. This requires that each all pass amplifier stage operate only on a limited portion of its frequency response characteristic that is essentially linear, requiring more individual stages than is economically desirable. These filters are not adapted to operation as minimum phase shift transversal filters, a characteristic that is highly desirable in an equalizer.
The use of a limited, finite number of stages in an all pass ladder network as proposed by Wiener and Lee results in truncation errors known in Fourier anaylsis as the "Gibbs phenomenon". The same basic problem occurs in connection with the Tattersall filters. The Wiener and Lee networks, and the Tattersall filters, are confined to real frequency responses; they do not extend to a minimum phase frequency response.
Calculation of the scaling coefficients for an equalizier network utilizing all pass operational amplifier circuits functioning as the equivalent of a substantial number of minimum phase shift transversal filters and having a specified frequency response characteristic covering a broad frequency range is extremely difficult and, indeed, virtually impossible. Another major difficulty in formulating an equalizer network of this type is encountered if it becomes necessary to modify the frequency response characteristic. Interactions between the individual stages of the equalizer network make determination of the necessary changes by mathematical analysis a practical impossibility. To some extent, these problems can be alleviated by an equalizer network that incorporates a multiplicity of individual filters; an equalizer of that kind can be economically acceptable and operationally desirable in some applications, particularly those involving continuing changes in frequency response requirements. This approach, however, results in an equalizer that is excessively complex, unduly costly, and substantially larger than desirable for many applications. At present, it appears that there is no known straightforward design technique adapted to development of an equalizer network having a minimum phase shift frequency response characteristic with a limited, practical number of stages that is capable of covering a broad frequency range, such as the full audio range, with minimum ripple and with little or no ringing from individual stages of the equalizer network.